Hotelling's Theorem

During the last two centuries there have been many periods of wide public concern that the economy was about to
collapse because some critical natural resource was about to be exhausted. Some of the resources people worried
about seem almost funny today: whale oil (used as a lighting fuel before the Civil War), timber, iron and coal
(now known to be very, very abundant). More recently, the focus has been on oil. Since the early twentieth century,
people have been worried that the world was using up its supply of oil much too fast. In the 1920's, for example,
the chief geologist of the U.S. Geological Survey predicted that U.S. oil reserves would be exhausted by 1934.

In a famous paper called "The Economics of Exhaustible Resources", Harold Hotelling pointed out that
deposits of exhaustible resources are an asset, just like money in the bank or shares of common stock. This simple
idea has an immediate and powerful implication: the owners of oil will want to sell oil when its price is rising
more slowly than the interest rate and hang on to their oil when its price is rising faster. In equilibrium, therefore,
oil prices should rise over time at a percentage growth rate equal to the interest rate. However, that is precisely
the condition for efficient allocation of oil over time. In other words, Hotelling showed that oil owners
have a powerful incentive -- their own profits -- for not using up their supplies of oil too fast.

If you want to read Hotelling's original paper, you can find it in the Journal of Political Economy, volume
39, pages 137-175, 1931. A link to the article in JSTOR appears below.